Addressing all the important past contributions in ILP is a tall order and given the limited space we will only focus on a few recent approaches that are in some ways relevant to our work. Among the ILP solvers that are capable of learning recursive predicates (in an explicit and symbolic manner), the most notable examples are Metagol ([1]}) and dILP ([2]}). Metagol is a powerful method that is capable of learning very complex tasks via using the user-provided meta-rules. The main issue with Metagol is that while it allows for some flexibility in terms of providing the meta-rules, it is not always clear how to define those meta formulas. In practice, unless the expert already has some knowledge regarding the form of the possible solution, it would be very difficult to use this method. dILP, on the other hand, is a neural ILP solvers that, like our method, uses propositionalization of the data and formulates a differentiable neural ILP solver. Our proposed algorithm is in many regards similar to dILP. However, because of the way it define templates, dILP is limited to learning simple predicates with arity of at most two and with maximum two atoms in each rule. CILP++ ([3]}) is another noticeable neural ILP solver which also uses propositionalization similar to our method and dILP. CLIP++ is a very efficient algorithm and is capable of learning large scale relational datasets. However, since this algorithm uses the bottom clause propositionalization, it is not able to learn recursive predicates.
In dealing with uncertain data and specially in the tasks involving classification of the relational datasets, the most notable framework is the probabilistic ILP (PILP) ([4]}) and its variants and also Markov Logic Networks (MLN) [5]}. These types of algorithms extend the framework of ILP to handle uncertain data by introducing a probabilistic framework. Our proposed approach is related to PILP in that we also associate a real number to each atom and each rule in the formula. We will compare the performance of our method to this category of statistical relational learners later in our experiment. The methods in this category in general are not capable of learning recursive predicates.
